Algebraic and Geometric Topology 1 (2001),
paper no. 32, pages 627-686.
Reshetikhin-Turaev invariants of Seifert 3-manifolds and a rational surgery formula
Soren Kold Hansen
Abstract.
We calculate the RT-invariants of all oriented Seifert manifolds
directly from surgery presentations. We work in the general framework
of an arbitrary modular category as in [V. G. Turaev, Quantum
invariants of knots and $3$--manifolds, de Gruyter Stud. Math. 18,
Walter de Gruyter (1994)], and the invariants are expressed in terms
of the S- and T-matrices of the modular category. In another direction
we derive a rational surgery formula, which states how the
RT-invariants behave under rational surgery along framed links in
arbitrary closed oriented 3-manifolds with embedded colored ribbon
graphs. The surgery formula is used to give another derivation of the
RT-invariants of Seifert manifolds with orientable base.
Keywords.
Quantum invariants, Seifert manifolds, surgery, framed links, modular categories, quantum groups
AMS subject classification.
Primary: 57M27.
Secondary: 17B37, 18D10, 57M25.
DOI: 10.2140/agt.2001.1.627
Submitted: 9 April 2001.
(Revised: 28 August 2001.)
Accepted: 5 September 2001.
Published: 30 October 2001.
Notes on file formats
Soren Kold Hansen
Institut de Recherche Mathematique Avancee,
Universite Louis Pasteur - C.N.R.S.
7 rue Rene Descartes, 67084 Strasbourg, France
Email: hansen@math.u-strasbg.fr
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